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  Canonical simplicial gravity

Dittrich, B., & Hoehn, P. A. (2012). Canonical simplicial gravity. Classical and quantum gravity, 29(11): 115009. doi:10.1088/0264-9381/29/11/115009.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-14D8-D Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-14DA-9
Genre: Journal Article

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1108.1974 (Preprint), 550KB
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 Creators:
Dittrich, Bianca1, Author              
Hoehn, Philipp A, Author
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Lattice, hep-lat
 Abstract: A general canonical formalism for discrete systems is developed which can handle varying phase space dimensions and constraints. The central ingredient is Hamilton's principle function which generates canonical time evolution and ensures that the canonical formalism reproduces the dynamics of the covariant formulation following directly from the action. We apply this formalism to simplicial gravity and (Euclidean) Regge calculus, in particular. A discrete forward/backward evolution is realized by gluing/removing single simplices step by step to/from a bulk triangulation and amounts to Pachner moves in the triangulated hypersurfaces. As a result, the hypersurfaces evolve in a discrete `multi-fingered' time through the full Regge solution. Pachner moves are an elementary and ergodic class of homeomorphisms and generically change the number of variables, but can be implemented as canonical transformations on naturally extended phase spaces. Some moves introduce a priori free data which, however, may become fixed a posteriori by constraints arising in subsequent moves. The end result is a general and fully consistent formulation of canonical Regge calculus, thereby removing a longstanding obstacle in connecting covariant simplicial gravity models to canonical frameworks. The present scheme is, therefore, interesting in view of many approaches to quantum gravity, but may also prove useful for numerical implementations.

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 Dates: 2011-08-092012
 Publication Status: Published in print
 Pages: 52 pages, 14 figures, 3 tables
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1108.1974
DOI: 10.1088/0264-9381/29/11/115009
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Title: Classical and quantum gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 29 (11) Sequence Number: 115009 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1